Ellingham-Horton 54-graph | Ellingham-Horton 78-graph

| vertex count | edge count | connected component count Ellingham-Horton 54-graph | 54 | 81 | 1 Ellingham-Horton 78-graph | 78 | 117 | 1

asymmetric | bicolorable | biconnected | bicubic | bipartite | bridgeless | class 1 | connected | cubic | cyclic | local | noncayley | nonempty | noneulerian | nonhamiltonian | nonplanar | perfect | perfect matching | regular | simple | square-free | traceable | triangle-free | uniquely colorable | unit-distance | weakly perfect | weakly regular

| complement graph name Ellingham-Horton 54-graph | (not a named graph) Ellingham-Horton 78-graph | (not a named graph)

| line graph name Ellingham-Horton 54-graph | (not a named graph) Ellingham-Horton 78-graph | (not a named graph)

| Ellingham-Horton 54-graph | Ellingham-Horton 78-graph vertex degrees | 3 (54 vertices) | 3 (78 vertices)

| radius | diameter | girth Ellingham-Horton 54-graph | 9 | 10 | 6 Ellingham-Horton 78-graph | 7 | 13 | 6 | vertex connectivity | edge connectivity Ellingham-Horton 54-graph | 3 | 3 Ellingham-Horton 78-graph | 3 | 3

| Ellingham-Horton 54-graph | Ellingham-Horton 78-graph characteristic polynomial | (x - 3) (x - 1)^2 x^4 (x + 1)^2 (x + 3) (x^2 - 3)^8 (x^6 - 2 x^5 - 8 x^4 + 10 x^3 + 19 x^2 - 4 x - 6) (x^6 + 2 x^5 - 8 x^4 - 10 x^3 + 19 x^2 + 4 x - 6) (x^8 - 4 x^7 - 5 x^6 + 30 x^5 + 3 x^4 - 68 x^3 + 3 x^2 + 46 x + 10) (x^8 + 4 x^7 - 5 x^6 - 30 x^5 + 3 x^4 + 68 x^3 + 3 x^2 - 46 x + 10) | (x - 3) (x - 1)^8 x^2 (x + 1)^8 (x + 3) (x^2 - 3)^6 (x^4 - 7 x^2 + 11)^2 (x^19 - 2 x^18 - 32 x^17 + 62 x^16 + 423 x^15 - 790 x^14 - 2995 x^13 + 5348 x^12 + 12317 x^11 - 20744 x^10 - 29807 x^9 + 46226 x^8 + 40917 x^7 - 55766 x^6 - 28781 x^5 + 30864 x^4 + 8190 x^3 - 4634 x^2 - 617 x + 204) (x^19 + 2 x^18 - 32 x^17 - 62 x^16 + 423 x^15 + 790 x^14 - 2995 x^13 - 5348 x^12 + 12317 x^11 + 20744 x^10 - 29807 x^9 - 46226 x^8 + 40917 x^7 + 55766 x^6 - 28781 x^5 - 30864 x^4 + 8190 x^3 + 4634 x^2 - 617 x - 204)

| chromatic number | edge chromatic number Ellingham-Horton 54-graph | 2 | 3 Ellingham-Horton 78-graph | 2 | 3

(-3)^1 (root of 10 - 46 x + 3 x^2 + 68 x^3 + 3 x^4 - 30 x^5 - 5 x^6 + 4 x^7 + x^8 near x = -2.88162)^1 (root of -6 + 4 x + 19 x^2 - 10 x^3 - 8 x^4 + 2 x^5 + x^6 near x = -2.84403)^1 (root of -6 + 4 x + 19 x^2 - 10 x^3 - 8 x^4 + 2 x^5 + x^6 near x = -2.36042)^1 (root of 10 - 46 x + 3 x^2 + 68 x^3 + 3 x^4 - 30 x^5 - 5 x^6 + 4 x^7 + x^8 near x = -2.30599)^1 (root of -6 - 4 x + 19 x^2 + 10 x^3 - 8 x^4 - 2 x^5 + x^6 near x = -2.03247)^1 (root of 10 + 46 x + 3 x^2 - 68 x^3 + 3 x^4 + 30 x^5 - 5 x^6 - 4 x^7 + x^8 near x = -1.96544)^1 (root of 10 - 46 x + 3 x^2 + 68 x^3 + 3 x^4 - 30 x^5 - 5 x^6 + 4 x^7 + x^8 near x = -1.83769)^1 (-sqrt(3))^8 (root of 10 + 46 x + 3 x^2 - 68 x^3 + 3 x^4 + 30 x^5 - 5 x^6 - 4 x^7 + x^8 near x = -1.52318)^1 (root of 10 - 46 x + 3 x^2 + 68 x^3 + 3 x^4 - 30 x^5 - 5 x^6 + 4 x^7 + x^8 near x = -1.47314)^1 (root of -6 - 4 x + 19 x^2 + 10 x^3 - 8 x^4 - 2 x^5 + x^6 near x = -1.21865)^1 (-1)^2 (root of 10 + 46 x + 3 x^2 - 68 x^3 + 3 x^4 + 30 x^5 - 5 x^6 - 4 x^7 + x^8 near x = -0.768061)^1 (root of -6 + 4 x + 19 x^2 - 10 x^3 - 8 x^4 + 2 x^5 + x^6 near x = -0.624496)^1 (root of -6 - 4 x + 19 x^2 + 10 x^3 - 8 x^4 - 2 x^5 + x^6 near x = -0.577822)^1 (root of 10 + 46 x + 3 x^2 - 68 x^3 + 3 x^4 + 30 x^5 - 5 x^6 - 4 x^7 + x^8 near x = -0.241758)^1 0^4 (root of 10 - 46 x + 3 x^2 + 68 x^3 + 3 x^4 - 30 x^5 - 5 x^6 + 4 x^7 + x^8 near x = 0.241758)^1 (root of -6 + 4 x + 19 x^2 - 10 x^3 - 8 x^4 + 2 x^5 + x^6 near x = 0.577822)^1 (root of -6 - 4 x + 19 x^2 + 10 x^3 - 8 x^4 - 2 x^5 + x^6 near x = 0.624496)^1 (root of 10 - 46 x + 3 x^2 + 68 x^3 + 3 x^4 - 30 x^5 - 5 x^6 + 4 x^7 + x^8 near x = 0.768061)^1 1^2 (root of -6 + 4 x + 19 x^2 - 10 x^3 - 8 x^4 + 2 x^5 + x^6 near x = 1.21865)^1 (root of 10 + 46 x + 3 x^2 - 68 x^3 + 3 x^4 + 30 x^5 - 5 x^6 - 4 x^7 + x^8 near x = 1.47314)^1 (root of 10 - 46 x + 3 x^2 + 68 x^3 + 3 x^4 - 30 x^5 - 5 x^6 + 4 x^7 + x^8 near x = 1.52318)^1 sqrt(3)^8 (root of 10 + 46 x + 3 x^2 - 68 x^3 + 3 x^4 + 30 x^5 - 5 x^6 - 4 x^7 + x^8 near x = 1.83769)^1 (root of 10 - 46 x + 3 x^2 + 68 x^3 + 3 x^4 - 30 x^5 - 5 x^6 + 4 x^7 + x^8 near x = 1.96544)^1 (root of -6 + 4 x + 19 x^2 - 10 x^3 - 8 x^4 + 2 x^5 + x^6 near x = 2.03247)^1 (root of 10 + 46 x + 3 x^2 - 68 x^3 + 3 x^4 + 30 x^5 - 5 x^6 - 4 x^7 + x^8 near x = 2.30599)^1 (root of -6 - 4 x + 19 x^2 + 10 x^3 - 8 x^4 - 2 x^5 + x^6 near x = 2.36042)^1 (root of -6 - 4 x + 19 x^2 + 10 x^3 - 8 x^4 - 2 x^5 + x^6 near x = 2.84403)^1 (root of 10 + 46 x + 3 x^2 - 68 x^3 + 3 x^4 + 30 x^5 - 5 x^6 - 4 x^7 + x^8 near x = 2.88162)^1 3^1

| Hosoya index | Kirchhoff index Ellingham-Horton 54-graph | 44 trillion | 2073 Ellingham-Horton 78-graph | 5.087×10^19 | 5648 | stability index | Wiener index Ellingham-Horton 54-graph | 82.02 trillion | 6937 Ellingham-Horton 78-graph | 1.609×10^20 | 18075